Properties of frame mappings devised by controlled p-frames and p-frames

Abstract

P-frames in Banach spaces are straightforward generalization of frames in Hilbert spaces. In this paper, motivated the concept of p-Bessel sequences, the concept of p-controlled Bessel sequences is introduced and showed that under some warily conditions, $1<p\leq 2$, they can use instead of each other. Also a close relationship between inherent properties of p-frame mappings and p-pseudo frame mappings with controlled p-frames and p-frames is found. In other words the cases that these natural mappings can be accretive, Lipschitz continuous, coercive and monotone are investigated.